Relay-feedback test

A relay-feedback test on the reactor temperature controller is used to obtain the ultimate gain and frequency (K, = 64 and Pv = 10 min), using a 50 K temperature transmitter span and assuming the maximum cooling water flow is twice the steady-state value. The Tyreus-Luyben settings give oscillatory response, so the controller gain is reduced by factor of 2 (Kc = 10, t = 1320 s). 

Relay feedback test %optr 0.25 l.i if errortt>0ioptr 0.25 0.9 tend fj fjss 4 optr ... 

There are two controllers. The proportional reactor level control has a gain of 5. The reactor temperature controller is tuned by running a relay-feedback test. The manipulated variable is the cooling water flowrate in the condenser. With a 50-K temperature transmitter span and the cooling water control valve half open at design conditions, the resulting tuning constants are Kc = 4.23 and = 25 min. 

Figure 3.49 Relay-feedback test with feed manipulation TR — F0.

The tuning of the temperature controller is achieved by mnning a relay-feedback test, which the recent versions of Aspen Dynamics has made quite easy to do. The button on the... 

Figure 3.77 Running relay-feedback test on temperature controller.

It is important to remember that a deadtime or several lags must be inserted in most control loops in order to mn a relay-feedback test. To have an ultimate gain, the process must have a phase angle that drops below —180°. Many of the models in Aspen Dynamics have only a first-order transfer function between the controller variable and the manipulated variable. In the CSTR temperature controller example, the controlled variable is reactor temperature and the manipulated variable is medium temperature. The phase angle of a first-order process goes to only —90°, so there is no ultimate gain. The relay-feedback test will fail without the deadtime element inserted in the loop. 

Figure 3.79 Relay-feedback test dynamic results.

The relay-feedback test results for the reactor temperature controller are shown in Figure 3.97. The Tyreus-Luyben controller settings are Kc = 2.25 and r, = 11.9 min. 

Figure 3.97 Relay-feedback test with LMTD.

Ziegler-Nichols (ZN) and Tyreus-Luyben (TL) PI tunings are evaluated. Ultimate gain and frequency are obtained by performing relay-feedback tests. Temperature control loops have three 20-s lags. The pressure control loop has two 30-s lags. There is a... 

Figure 6.63 shows this new control structure. The setpoint of the temperature controller TC2 is 392 K, and it is direct-acting. With a deadtime of 1 min and a temperature transmitter range of 350-450 K, the relay-feedback test gives Tyreus-Luyben settings of Kc = 14.6 and tj = 10.6 min. Figure 6.64 shows the response of the closedloop system... 

All controllers are PI except for the drum level controller, which is P only. Two 0.5-min lags are assumed in the pressure loop. Three 0.1-min lags are assumed in the temperature loops. Relay-feedback tests are conducted to get the ultimate gain and period, and the Tyreus-Luyben settings are used. 

Control with Only Bypass The important control loop in this process is the temperature controller that manipulates the bypass flow to control the temperature of the mixed hot and cold streams. The controller is direct acting (an increase in temperature opens the bypass valve). A 1-min deadtime is inserted in the loop, and a relay-feedback test is run that gives Tyreus-Luyben settings Kc = 0.48 and T/ = 4.0 min. The temperature transmitter span is 350-450 K. 

The next part involves controller tuning. We must determine the tuning constants for the controllers in the plant. While this task is often performed by using heuristics and experience, it can sometimes be a nontrivial exercise for certain loops. We recommend using a relay-feedback test that determines the ultimate gain and period for the control loop, from which controller settings can be calculated (Luyben and Luyben, 1997). 

Figures 6.14 and 6.15 give dynamic responses of the tray temperatures, reboiler heat input, and bottoms product impurity. The temperature loops were tuned using the TL (Tyreus-Luyben) tuning rules after the ultimate gain and ultimate frequency had been determined using a relay-feedback test. Two 0.5-minute first-order lags are used in the temperature loop. Temperature transmitter spans are 100T. The ultimate gain and period for the tray 6 temperature loop are 4.2 and 2.7 minutes, and for the tray 14 loop are 12.7 and 2.5 minutes. These results reflect the fact that the process gain is higher when tray 6 is...

The critical product-quality and safety-constraint loops were tuned by using a relay -feedback test to determine ultimate gains and periods. The Tyreus-Luyben PI controller tuning constants were then implemented. Table 11.12 summarizes transmitter and valve spans and gives controller tuning constants for the important loops. Proportional control was used for all liquid levels and pressure loops. 

Perform a relay-feedback test on each temperature, pressure, and... 

The examples presented in this chapter illustrate these various steps. Once the control structure has been selected, dynamic simulations of the entire process can be used to evaluate controller performance. Commercial software is being developed that will facilitate plantwide dynamic simulation studies. To tune controllers, each individual unit operation can be isolated and controllers tuned using the relay-feedback test (discussed in Chapter 16). 

If the input U does not provide enough excitation of the process over the important frequency range, the model fidelity is poor, particularly in processes with appreciable noise. This is why direct sine wave testing at a frequency near the ultimate frequency and relay feedback testing are such usefril methods. 

Once the relay feedback test has been, performed and the ultimate gain and ultimate frequency have been determined, we may simply use the results to calculate controller setting. Alternatively, it is possible to use this information to calculate -proximate transfer functions. The idea is to pick a very simple form for the transfer function and hnd the parameter values that fit the ATV results. 

Using the MATLAB Identification Toolbox and PRBS test signals is much more complex than using simple step tests or relay feedback tests. Much more data are required and the analysis is more difficult. However, the PRBS method is probably better in situations where the signals from the process are heavily corrupted by noise that cannot be simply filtered out. 

This chapter has illustrated several identification methods that are used to determine dynamic parameters or models from experimental plant data. The simple and effective relay feedback test is a powerful tool for practical identification if the objective is the design of feedback controllers. The more complex and elegant statistical methods are currently popular with the theoreticians, but they require a very large amount of data (long test periods) and their effective use requires a high level of technical e q3ertise. It is very easy to get completely inaccurate results from these sophisticated tests if the user is not aware of all the potential pitfalls (both fundamental and numerical). 

We strongly recommend the use of the simplest method that does the job. In most applications the tool of choice is the relay feedback test (ATV). It is quick, simple, and accurate, and it works to accomplish its goal. What more could be asked of a practical tool ... 

Using the simulation program given in Appendix A for the three-heated-tank process and a relay feedback test, determine the ultimate gain and ultimate frequency for the loop in which the temperature in the third tank T3 is controlled by manipulating the heat input to the first tank Qi. Compare these results with the theoretical values obtained in Example 8.8. 

Relay-Feedback Test. Everything is ready for the relay-feedback test. Clicking the Tune button on the far right at the top of the controller faceplates (see Fig. 7.25) opens the window shown in Figure 7.26a. We specify a Closed loop ATV as... 

Figure 7.26 (a) Setting up the relay-feedback test, (h) Relay-feedback test results, (c) Calculated controller settings. 

After the simulation is run, a 3 min deadtime is inserted. Initialization and Dynamic runs are made to converge to steady-state conditions. Then a relay-feedback test is run. Results are shown in Figure 7.31. Notice that the timescale on the plot is much different than for the temperature controller. The ultimate gain is 0.547 and the ultimate period is 33.6 min. The Tyreus-Luyben settings are calculated and inserted in the composition controller. The flowsheet is given in Figure 7.32. 

The final control structure is shown in Figure 7.46. Both the R/F and the QR/F ratios are installed. Of course the temperamre controller must be retuned. Relay-feedback testing and Tyreus-Luyben tuning give Kc = 1.96 and ti = 11.9 min. The composition controller also must be retuned but changes only slightly. 

The tray temperature controllers are tuned by inserting a 1 min deadtime in the loop and using the relay-feedback test to determine the ultimate gain and ultimate frequency. Then, the Tyreus-Luyben settings are used. Table 8.2 gives the tuning constants. 

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